A property of sequential control processes

by Ralph E. Strauch, Arthur F. Veinott

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An observation of a discrete time Markov control process having a finite number of states and possible decisions. Derman (Ann. Math. Stat., 35, 1964) has shown that, for criteria involving limiting average probabilities of visits to state-decision pairs, we need only consider initial randomizations of nonrandom stationary rules. It is shown that there is a rule which induces the same probability on the precess as any initial randomization; hence nothing new is introduced by initial randomization. An observation of a discrete time Markov control process having a finite number of states and possible decisions. Derman (Ann. Math. Stat., 35, 1964) has shown that, for criteria involving limiting average probabilities of visits to state-decision pairs, we need only consider initial randomizations of nonrandom stationary rules. It is shown that there is a rule which induces the same probability on the process as any initial randomization; hence nothing new is introduced by initial randomization. 15 pp.

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